The present invention relates generally to methods for designing and optimizing the number, placement, and size of fractures in a subterranean formation and more particularly to methods that account for stress interference from other fractures when designing and optimizing the number, placement, and size of fractures in the subterranean formation.
One method typically used to increase the effective drainage area of well bores penetrating geologic formations is fracture stimulation. Fracture stimulation comprises the intentional fracturing of the subterranean formation by pumping a fracturing fluid into a well bore and against a selected surface of a subterranean formation intersected by the well bore. The fracturing fluid is pumped at a pressure sufficient that the earthen material in the subterranean formation breaks or separates to initiate a fracture in the formation.
Fracture stimulation can be used in both vertical and horizontal wells. Fracturing horizontal wells may be undertaken in several situations, including situations where the formation has:                1. restricted vertical flow caused by low vertical permeability or the presence of shale streaks;        2. low productivity due to low formation permeability;        3. natural fractures in a direction different from that of induced fractures, thus induced fractures have a high chance of intercepting the natural fractures; or        4. low stress contrast between the pay zone and the surrounding layers. In the fourth case, a large fracturing treatment of a vertical well would not be an acceptable option since the fracture would grow in height as well as length. Drilling a horizontal well and creating either several transverse or longitudinal fractures may allow rapid depletion of the reservoir through one or more fractures.        
Shown in FIG. 1 is an example of a well bore, represented generally by the numeral 100, comprising a generally vertical portion 102 and two laterals 104 and 106. The generally vertical portion 102 is drilled in a generally vertical direction, and the laterals 104 and 106 are disposed at angles 108 and 110, respectively to the vertical portion 102. The well bore 100 is referred to as a horizontal well because it has one or more laterals (in the case of well 100, laterals 104 and 106). Typically, only the laterals 104 and 108 are open for production in a horizontal well. If the well 100 only had a generally vertical portion 102, it would be referred to as a vertical well. Typically, all production in a vertical well comes from the generally vertical portion 102.
Shown in FIG. 2 is a perspective view of the well bore 100 comprising lateral 104. The lateral 104 comprises three fractures 202, 204 and 206. Depending on the orientation of the lateral 204 to the direction of minimal stress, the fractures 202, 204 and 206 may be transverse or axial fractures. If the lateral 104 is drilled in direction of minimal stress, then the fractures 202, 204 and 206 are orientated perpendicular to the direction of minimal stress and are referred to as transverse fractures. If the lateral 104 is drilled perpendicular to the direction of minimal stress, then the fractures 202, 204 and 206 are orientated parallel to the direction of minimal stress and are referred to as axial fractures.
Each of the fractures 202, 204 and 206 typically has a narrow opening that extends laterally from the well bore. To prevent such opening from closing completely when the fracturing pressure is relieved, the fracturing fluid typically carries a granular or particulate material, referred to as “proppant,” into the opening of the fracture and deep into the fracture. This material remains in each of the fractures 202, 204 and 206 after the fracturing process is finished. Ideally, the proppant in each of the fractures 202, 204 and 206 holds apart the separated earthen walls of the formation to keep the fracture open and to provide flow paths through which hydrocarbons from the formation can flow into the well bore at increased rates relative to the flow rates through the unfractured formation. Fracturing processes are intended to enhance hydrocarbon production from the fractured formation. In some circumstances, however, the fracturing process may terminate prematurely, for a variety of reasons. For example, the “pad” portion of the fracturing fluid, which is intended to advance ahead of the proppant as the fracture progresses, may undesirably completely “leak off” into the formation, which may cause the proppant to reach the fracture tip and create an undesirable “screenout” condition. Thus, properly predicting fracture behavior is a very important aspect of the fracturing process.
In the past, fracturing typically took place in well bores that were cased and perforated. The total number of fractures was a limited number per lateral in the case of fracturing horizontal wells and the fractures had sufficient space between each other such that stress interference between the fractures was minimal. With the advent of new fracturing technologies such as SURGIFRAC provided by Halliburton Energy Services, fractures may be placed in open hole well bores. Furthermore, it is now feasible and cost-effective to place many more fractures in a well bore. When many fractures are induced in a well bore, the geomechanical stress caused by fractures on each other can no longer be ignored. Current fracturing modeling methods, however, do not account for geomechanical stresses caused by one fracture on another.